Basic properties
Modulus: | \(4016\) | |
Conductor: | \(4016\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
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Order: | \(500\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
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Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
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Galois orbit 4016.bs
\(\chi_{4016}(29,\cdot)\) \(\chi_{4016}(37,\cdot)\) \(\chi_{4016}(53,\cdot)\) \(\chi_{4016}(61,\cdot)\) \(\chi_{4016}(77,\cdot)\) \(\chi_{4016}(109,\cdot)\) \(\chi_{4016}(133,\cdot)\) \(\chi_{4016}(141,\cdot)\) \(\chi_{4016}(165,\cdot)\) \(\chi_{4016}(213,\cdot)\) \(\chi_{4016}(229,\cdot)\) \(\chi_{4016}(269,\cdot)\) \(\chi_{4016}(277,\cdot)\) \(\chi_{4016}(285,\cdot)\) \(\chi_{4016}(293,\cdot)\) \(\chi_{4016}(333,\cdot)\) \(\chi_{4016}(341,\cdot)\) \(\chi_{4016}(349,\cdot)\) \(\chi_{4016}(381,\cdot)\) \(\chi_{4016}(397,\cdot)\) \(\chi_{4016}(413,\cdot)\) \(\chi_{4016}(421,\cdot)\) \(\chi_{4016}(429,\cdot)\) \(\chi_{4016}(437,\cdot)\) \(\chi_{4016}(453,\cdot)\) \(\chi_{4016}(461,\cdot)\) \(\chi_{4016}(485,\cdot)\) \(\chi_{4016}(493,\cdot)\) \(\chi_{4016}(557,\cdot)\) \(\chi_{4016}(573,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{500})$ |
Fixed field: | Number field defined by a degree 500 polynomial (not computed) |
Values on generators
\((2511,3013,257)\) → \((1,-i,e\left(\frac{153}{250}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 4016 }(61, a) \) | \(-1\) | \(1\) | \(e\left(\frac{21}{500}\right)\) | \(e\left(\frac{31}{100}\right)\) | \(e\left(\frac{69}{250}\right)\) | \(e\left(\frac{21}{250}\right)\) | \(e\left(\frac{441}{500}\right)\) | \(e\left(\frac{317}{500}\right)\) | \(e\left(\frac{44}{125}\right)\) | \(e\left(\frac{36}{125}\right)\) | \(e\left(\frac{3}{500}\right)\) | \(e\left(\frac{159}{500}\right)\) |